Closed, Re exive, Invertible, and Normal Subhypergroups of Special Hypergroups

Authors

  • Pavlina Rackova University of Defence, Brno, Czech Republic

Keywords:

Hypergroup, transposition hypergroup, join space, closed, re exive, invertible, and normal subhypergroup, quasiordered group, quasiorder hypergroup.

Abstract

In [5] J. Jantosciak introduced several special types of subhyper-groups (invertible, closed, normal, re exive) of a general hypergroup and studied their relationship. In this article, the full description of such subhypergroups in hypergroups induced by quasiordered groups is given. Further, it is shown that there are no such non-trivial sub-hypergroups in quasiorder hypergroups.

References

Corsini, P., Leoreanu, V., Applications of Hyperstructure Theory. Kluwer AP, Dordrecht, Boston, London 2003, 322 pp.

Hoskova, S., Representation of quasi-order hypergroups. Global Journal of Pure and Applied Mathematics, vol. 1, Number 2, India (2005), pp. 173-176.

Chvalina, J., Funkcionaln grafy, kvaziusporadane mnoziny a komutativn hypergrupy. Brno, MU 1995, 206 pp. (in Czech)

Jantosciak, J., Transposition in hypergroups. Internat. Congress on AHA 6 (Prague 1996), Democtritus Univ. of Thrace Press, Alexandropolis, 1997, pp. 77-84.

Jantosciak, J., Transposition hypergroups: Noncommutative join spaces. J. Algebra 187 (1997), pp. 97-119.

Rackova, P., Akce polohypergrup a modelovan hypergrup integraln mi operatory. PhD. Thesis, Faculty of Science, Palacky University, Olomouc 2008, Czech Rep., 73 pp. (in Czech)

Rackova, P., Hypergroups of symmetric matrices. 10th International Congress on AHA (Brno 2008), Proceedings, pp. 267{271, ISBN 978-80-7231-688-5.

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Published

2012-12-18

Issue

Vol. 23 (2012)

Section

Volume 23-2012

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